Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?
Answers
.. = -20/-√841 . . . . . . . . . . . . . . . . . θ is a 4th-quadrant angle, so cos(θ) > 0
.. = 20/29
The value of the cosine is 20/29.
Answer:
The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Step-by-step explanation:
It is given that an angle θ with the point (−20, −21) on its terminating side.
It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]hypotenuse^2=(20)^2+(21)^2[/tex]
[tex]hypotenuse^2=400+441[/tex]
[tex]hypotenuse^2=841[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{841}[/tex]
[tex]hypotenuse=29[/tex]
In a right angled triangle,
[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]
[tex]\cos \theta=\frac{20}{29}[/tex]
θ lie in the third quadrant and cosine is negative in third quadrant.
[tex]\cos \theta=-\frac{20}{29}[/tex]
Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Related Questions
Trey wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 31
feet and its width is 24
feet. Suppose each pack of seed covers 12
square feet. How many packs of seed will he need to cover the backyard?
Answers
Area of a rectangle is length x width.
31 x 24 = 744
Divide the total area of the yard by the coverage of the seeds.
744/12 = 62
He will need 62 packs of seed.
To find out how many packs of seeds Trey needs, we need to first determine the area of his backyard which is 744 square feet. Each pack of seed cover 12 square feet. Therefore, dividing the total area by the area a pack of seed covers, we find that he needs 62 packs of seeds.
Explanation:The subject of this question is Mathematics. Specifically, it involves the concept of area and multiplication, commonly taught in middle school. Trey's backyard is in the shape of a rectangle, and we know that the area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 31 feet and the width is 24 feet. Multiplying these numbers gives us a total area of 744 square feet.
Each pack of seed covers 12 square feet. So, to figure out how many packs Trey needs, we would divide the total area by the area each pack covers. Dividing 744 by 12 gives us 62, which means Trey will need to buy 62 packs of seeds.
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How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Answers
_______________________________________________
XY = 3 units (obtained from counting on the graph provided).
YZ = 5 units (obtained from counting on graph provided).
_______________________________________________
To find ZX (the hypotenuse); use the Pythogorean Theorem:
→ 3² + 5² = c² ; in which "c" = ZX ;
→ c² = 3² + 5² = 9 + 25 = 34 ;
→ c² = 34 ;
To find "c" ; take the positive square root of each side of the equation;
to isolate "c" on one side of the equation; & to solve for "c" ;
→ √(c²) = √34 ;
→ c = 5.8309518948453005 ;
→ round to: "5.831 "
_______________________________________________________
At a sale, books are sold at $90.75 each, which is 75 percent of the original price. What is the original price
Answers
[tex] \frac{75}{100} = \frac{90.75}{x} \\ x = \frac{90.75 \times 100}{75} = \frac{9075}{75} = 121[/tex]
the answer is 121
To find the original price of the book, we can set up an equation: 0.75x = $90.75. Solving for x, we find that the original price is $121.
Explanation:To find the original price of the book, we can set up an equation. Let's denote the original price as x. The sale price is 75% of the original price, which can be expressed as 0.75x. We are given that the sale price is $90.75, so we can set up the equation:
0.75x = $90.75
To solve for x, we divide both sides of the equation by 0.75:
x = $90.75 / 0.75
Using a calculator, we can calculate that the original price of the book is $121.
Choose the equation of the vertical line passing through the point (-2, 3).
y = 3
x = 3
y = -2
x = -2
Question 10 (Multiple Choice Worth 5 points)
[4_05]Choose the equation of the horizontal line that passes through the point (-5, 1).
y = -5
x = 1
y = 1
x = -5,
Answers
a) = -2
b) = 1
What is the sum of 11 feet and 4 yards?
8 yards
15 feet
23 feet
8 yards, 1 foot
Answers
3 × 4 = 12
12 + 11 = 23
The answer is 23 ft.
Hope this helps!
What is the length of ST, to the nearest tenth of a yard?
Answers
Use the Law of Sines to find side b.
b / sin(B) = a / sin(A)
b / sin(59°) = 7 / sin(79°)
b = (sin(59°) x 7) / sin(79°)
b = 6.112
That is answer B.) 6.1 yards
Hope this helps!
Answer: Second Option is correct.
Step-by-step explanation:
Since we have given that
ΔSRT is a triangle with measures :
SR = 7 yd
∠T = 79°
∠R = 59°
We need to find the side ST say x.
We will use " Law of Sines " :
[tex]\frac{\sin T}{SR}=\frac{\sin R}{ST}\\\\\frac{\sin 79^\circ}{7}=\frac{\sin 59^\circ}{x}\\\\0.14=\frac{\sin 59^\circ}{x}\\\\x=\frac{\sin 59^\circ}{0.14}\\\\x=6.12\ yd[/tex]
Hence, the length of ST = 6.1 yd.
Therefore, Second Option is correct.
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 8m? Enter your answer in the box
Answers
What is 2 ¾% in decimal form?
Answers
2 3/4 = 2 + 3/4
2 + ( 3 ÷ 4 )
2 + 0.75 = 2.75
Hope this helped!
Roberto will save 1/6 of his allowance each day. If he gets $2.00a day, about how much money will be save each day? Round your answer to the nearest penny.
Answers
Which expression is equivalent to -18a^-2 b^5/-12a^-4 b^-6? Assume a=0, b=0.
a- 2a^2 b^11/3
b-2a^2 b^30/3
c-3a^2 b^11/2
d-3a^2 b^30/2
Answers
coefficients: 18/-12 = -3/2
exponents of a: -2-(-4)=2
exponents of b: 5-(-6)=11
The required expression is (-3/2)a²b¹¹ which is equivalent to the given expression. which is the correct answer would be option (C)
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:
-18a⁻² b⁵/-12a⁻⁴ b⁻⁶
To find the equivalent expression for -18a⁻² b⁵/-12a⁻⁴ b⁻⁶, we need to combine the constants and factors that have the same base and exponent.
You can begin by combining the constants in the fraction: -18/-12 = -3/2.
Next, you can simplify the terms involving the variables. Recall that when you divide two powers with the same base, you subtract the exponents. Therefore, you can simplify the expression as follows:
(-3/2)(a⁻² ÷ a⁻⁴ (b⁵ ÷ b⁻⁶)
= (-3/2)(a⁻⁴ a⁴) (b⁵ b⁶)
= (-3/2)(a²)(b¹¹)
= (-3/2)a²b¹¹
This is the simplified form of the given expression.
Hence, the correct answer would be option (C)
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: Below are two expressions. Simplify each and then choose the statement that is true.
Expression #1
Expression #2
Expression 1: (3x2)3x^2
Expression 2: (3x^3)^2(x^2)
The exponents in Expression #1 are greater than the exponents of Expression #2.
The exponents on Expression #2 are greater than the exponents of Expression #1.
The exponents of Expression #1 are the same as the exponents of Expression #2.
The relationship cannot be determined with the given information.
The answer I got was A
Answers
We have then:
Expression 1:
(3x2) 3x ^ 2
(9x ^ (2 + 2))
9x ^ 4
Expression 2:
(3x ^ 3) ^ 2 (x ^ 2)
(9x ^ 6) (x ^ 2)
(9x ^ (6 + 2))
9x ^ 8
Answer:
The exponents on Expression # 2 are greater than the exponents of Expression # 1.
(8> 4)
1/3 of birds egg hatch in two eggs hatch how many eggs did the bird lay
Answers
2/3 is 4.
3/3 is 6.
Hope this helped☺☺
The total number of eggs a bird laid is 6 eggs.
To solve this problem we need to break it down step by step:
Assuming 1/3 of the eggs hatch means 2 eggs hatch, so if two eggs hatch, this represents 1/3 of the total eggs laid.
To find the total number of eggs the bird laid, we need to find the equivalent of 1 whole (the total). If 1/3 is equal to 2 eggs, then the whole (3/3 or 1) would be 6 eggs.
60 PTS, Will Mark Brainliest
Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.
Answers
1 and 5 are corresponding angles
2 and 6 are corresponding angles
2 and 7 are alternate exterior
3 and 5 are alternate interior
3 and 6 are consecutive interior
3 and 8 are corresponding
4 and 5 are consecutive interior
4 and 6 are alternate interior
4 and 7 are corresponding
Answer ASAP
Find the area for this shape
Answers
so...
A = 1/2(4.9 + 1.5)(4)
A = 1/2(6.4)(4) = [tex]12.8 km^{2}[/tex]
A = [tex] \frac{a+b}{2} (h)[/tex]
A = [tex] \frac{1.5+4.9}{2} (4) [/tex]
A = 12.8
The area is 12.8 km²
Evaluate: f(x) = -2x – 3 for x = -1. A. -5 B. -2 C. -1 D. 5
Answers
A small software company has two customer service representatives.The supervisor of he customer service department determines that there is an 85% probabiiy that a customer sevice representative will e on the phone with a customer at any given time. what is the probability o both representatives being on the the phone at the same time?,
Answers
Answer:
The probability that both customer representatives are on the phone at the same time is 72.25%.
Step-by-step explanation:
Consider the provided information.
There is an 85% probability that a customer service representative will be on the phone with a customer at any given time.
There are 2 customer service representatives.
To find the probability that both customer representatives are on the phone at the same time, we multiply the independent probabilities together.
0.85×0.85=0.7225
Hence, the probability that both customer representatives are on the phone at the same time is 72.25%.
The measure of an angle is 45°. what is the measure of a supplementary angle?
Answers
45 + x = 180
x = 135
so the answer is 135°.
help please.
1. Oatmeal costs $1.73/lb.
How much would 2.6 lb of oatmeal cost?
(Points : 1)
$1.50
$4.48
$4.50
$4.58
Question 2. 2. What percent of $520 is $494?
(Points : 1)
5%
11%
26%
95%
Answers
1.73/lb * 2.6 pounds= $4.498= $4.50
ANSWER: C) $4.50
2) set up a proportion. 494 is what % out of 520 as x is what out of 100.
$494/$520= x/100
cross multiply
(494*100)= (520*x)
49400= 520x
divide both sides by 520
95%= x
ANSWER: D) 95%
Hope this helps! :)
1. Cost of oatmeal:
Cost of oatmeal=1.73/lb× 2.6 pounds
Cost of oatmeal= $4.498
Cost of oatmeal= $4.50 (Approximately)
2. Percentage:
Percentage=494/520×100
Percentage=95%
Inconclusion the amount that 2.6 lb of oatmeal cost is $4.50 and the percent of $520 that is $494 is 95%.
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Mickey’s beagle has a mass of 15 kilograms. His dachshund has a mass of 13 kilograms. What is the combination of both?
Answers
Wich fraction is equivalent to negative 7 over 8
Answers
John has opened 8 gifts and 6 of them have been toys. What is the probability that the next Gift ?he opens will be a toy
Answers
6:8=3/4.
John has a 3/4 probability of opening another toy.
Hope this helps!
What is the locus of all points equidistant from lines X and Y in the figure?
Answers
More details about X and Y in this question would be really helpful!
Please Help me !!Q 1,2,3
Answers
1i) (20 cm)*(12 cm) = 240 cm^2
2ii) (7 cm)*(7.5 cm) = 52.5 cm^2
3iii) 27 cm^2 = (6 cm)*h
.. h = (27 cm^2)/(6 cm) = 4.5 cm
what’s the answer to
2(x+6) + 3x +4
Answers
2x + 12 + 3x + 4
Next, combine all like terms (terms with x, and terms without x).
5x + 16
That is the final answer, because it cannot be simplified any further. Hope this helps!
A regular hexagon has a perimeter of 120 m. Find its area. Leave your answer in simplest radical form.
Answers
(1/2) • a • p
Where a is the apothem (a line from the center of a side to the center of the shape) and p is the perimeter.
We have the perimeter: 120
Now to find the apothem. To find it, we’re going to cut any sidelength in half, and the line from that half to the center of the hexagon will form a right triangle. We know the bottom leg (where the shape is) is 10 (since 120/6 = 20, and we cut that in half). All we need is angles. To find the interior angle of any regular shape, we use
(180(n - 2))/n
Plugging in, we get 120 degrees for every side. Since we cut it in half, then the top angle of our right triangle is 60. You know what that means? We’ve just found a 30, 60, 90 triangle.
Using the laws of this special triangle, the length of the apothem is the shortest leg times sqrt(3)
So, 10sqrt(3) is your apothem.
Plug everything in!
(1/2) • a • P
(1/2) • 10sqrt(3) • 120
Your area is 600sqrt(3)
Which object would be best measured in ounces?
A.
strawberry
B.
bed
C.
car
D.
horse
Answers
The temperature of a cup of coffee t minutes after it has been poured is described by the function C(t) = 20 + 60(0.95)^t . a. How many minutes does it take for the coffee to cool to a temperature of d degrees? b. About how fast is the temperature dropping when t = 1?
Answers
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 30 minutes after it was poured is:
F = 120 ( 2 ^ -30/10) + 60
F = 120 * 1/ 8 + 60
F = 15 + 60
F = 75
A basketball player scores 162 points in 9 games. at this rate, how many points will she score in a 24-game season? answer
Answers
162/9 = 18 points per game
18 points x 24 games = 432
What is the value of tan D?
Answers
As according to the mathematical acronym SOH CAH TOA (Sin Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent), the correct answer would be the first choice, [tex] \frac{12}{5} [/tex].
The reason behind this is because the tangent value of an angle is always the length value opposite of given angle over the value adjacent (or right next to) the given angle.
In this case, the question is asking for Tan D. The side value opposite of angle D would be 12, and the length value that is adjacent to angle D is 5.
Therefore, the value of tan D would be [tex] \frac{12}{5} [/tex].
Hope this helps and I hope you have a marvelous day! :)
The value of tan D would be as follows:
[tex]\frac{12}{5}[/tex]Find the value of TanGiven that,
A right-angled triangle EFD,
As we know,
Tan = Opposite sides' length/adjacent sides' length
So,
it is given that,
The length of the opposite side = 12
Adjacent Side's length = 5
∵ The value of Tan D [tex]= 12/5[/tex]
Thus, the above-mentioned answer is correct.
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use the graph for all 3 question
1) Henry, a 41-year-old male, bought a $100,000, 10-year life insurance policy through his employer. Henry is paid biweekly. what is his annual life insurance premium?
A)$455
B)$578
C)$1033
D)$1368
2) Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy though her employer. Karen is paid weekly. How much is deducted from her paycheck for life insurance?
A)$10.86
B)$25.33
C)$35.12
D)$50.65
3) Nikos, a 39-year-old male, bought a $300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 year of coverage?
A)$13,650
B)$27,300
C)$30,990
D)$61,980
Answers
1.) Henry- $578
2.) Karen- $25.33
3.) Nikos- $61,980
Hope it helps!(:
Answer:
1: B) $578
2: B) $25.33
3: D) $61,980
Step-by-step explanation:
1) Henry's premium = ($100,000 / $1,000) x $5.78 = $578
2) Karen's total premium = ($75,000 / $1,000) x $17.56 = $1,317
if she is paid weekly, then the premium must be divided by 52 weeks = $1,317 / 52 weeks = $25.33 deducted per week
3) Nikos's premium per year = ($300,000 / $1,000) x $10.33 = $3,099
times 20 years = $3,099 x 20 = $61,980